https://neckpinch.com/authors/minhyun-kim/New arXiv papers by Minhyun Kim, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2304.11617/arxiv:2304.11617Sun, 23 Apr 2023 00:00:00 GMTKyeongsu Choi, Minhyun Kim, Taehun Lee — We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure μ with a positive smooth density f, any solution to the Lₚ Minkowski problem in ℝⁿ⁺¹ with p ≤ −n+2 is a hypersurface of class C^(1,1). This is a sharp result because for each p∈ [−n+2,1) there exists a convex hypersurface of class C^(1,1/(n+p-1)) which is a solution to the Lₚ Minkowski problem for a positive smooth density f. In particular, the C^(1,1) regularity is optimal in the case p=−n+2 which includes the logarithmic Minkowski problem in ℝ³.Other curvature flowsGauss curvature flowAnisotropic & nonlocal flows